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## Homework Statement

A uniform thin disk rolls without slipping on a plane and a force is being applied at its center parallel to the plane. Find the lagrangian and thereby the generalized force.

## Homework Equations

Lagranges equation.

## The Attempt at a Solution

This is my first ever exercise of this kind. We first note that U=0 so the lagrangian is simply L=T. We then want to express the kinetic energy T in terms of coordinates, which contain the constraints of the motion implicitly. Therefore we should use polar coordinates. Correct so far?

We then get:

L = T = ½m([itex]\omega[/itex]

^{2}r

^{2}) (1)

And now lagranges equation says:

d/dt[dT/dq

_{j}'] - dT/dq

_{j}= Q

_{j}

where Q

_{j}is the generalized force. There is for this motion one equation of the above kind - one for theta and one for r.

Should I now just differentiate with respect to r and [itex]\theta[/itex] and make two separate equations of the above kind of which I can find the components of the generalized force?

I just don't get anything very sensible when I differentiate the expression for L above with the two variables, and when my teacher did it I think he just differentiated with respect to x - why is that? Shouldn't you use the generalized coordinates?